We examine several theories that describe how stellar magnetic fields on classical T Tauri stars (CTTSs) interact with their surrounding accretion disks. We demonstrate that these theories require magnetic field strengths ranging from a few hundred to several thousand gauss, depending on which model is used and more importantly on the properties of individual systems. For example, the CTTS BP Tau is predicted to have a relatively strong magnetic field (1.4-4.1 kG), which should be detectable. We present infrared (IR) and optical echelle spectra of BP Tau and several reference stars of similar spectral class. Using detailed spectrum synthesis and the latest model atmospheres, we fitted 12 absorption features in the optical spectrum, including the strong titanium oxide (TiO) band head at 7055 A. For BP Tau we determine key stellar parameters: effective temperature (Teff=4055 ± 112 K), gravity (log g=3.67 ± 0.50), metallicity ([M/H]=0.18 ± 0.11), projected rotational velocity (v sin i=10.2 ± 1.8 km s-1), and optical veiling (r=0.00-0.15). A similar analysis of 61 Cyg B (K7 V) is used to validate the methodology. We then use the IR spectra to look for Zeeman broadening, which has a more pronounced effect at longer wavelengths. A Zeeman sensitive Ti I line at 2.2233 μm appears significantly broadened in BP Tau, relative to several rotationally broadened standard stars. The observed line is also significantly broader than predictions based on our optical analysis. Interpreting this excess broadening as Zeeman splitting of the Ti I line, we fitted the spectrum and find a distribution of field strengths whose surface averaged mean is =2.6 ± 0.3 kG. We did not use the Zeeman sensitive Fe I line at 8468.4 A when determining stellar or magnetic parameters for BP Tau, so this line provides a test of our results. The observed line profile is indeed broader than the nonmagnetic prediction, but the 8468.4 A line gives a magnetic flux lower than what was obtained in the IR, perhaps indicating that strong fields are concentrated into cool spots. Finally, we investigate an ad hoc model in which the IR line is assumed to form in the accretion disk itself. We discuss several reasons why the magnetic model is preferred, but the disk atmosphere example illustrates that our magnetic field measurement must still be tested using several IR lines with a range of Zeeman sensitivities.